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@ -1,573 +0,0 @@
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
% Beamer Presentation
|
||||
% LaTeX Template
|
||||
% Version 1.0 (10/11/12)
|
||||
%
|
||||
% This template has been downloaded from:
|
||||
% http://www.LaTeXTemplates.com
|
||||
%
|
||||
% License:
|
||||
% CC BY-NC-SA 3.0 (http://creativecommons.org/licenses/by-nc-sa/3.0/)
|
||||
%
|
||||
% Changed theme to WSU by William King
|
||||
%
|
||||
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
|
||||
%----------------------------------------------------------------------------------------
|
||||
% PACKAGES AND THEMES
|
||||
%----------------------------------------------------------------------------------------
|
||||
|
||||
\documentclass[xcolor=dvipsnames,aspectratio=169]{beamer}
|
||||
|
||||
|
||||
%Import Preamble bits
|
||||
\input{../assets/preambles/FormattingPreamble.tex}
|
||||
\input{../assets/preambles/TikzitPreamble.tex}
|
||||
\input{../assets/preambles/MathPreamble.tex}
|
||||
\input{../assets/preambles/BibPreamble.tex}
|
||||
\input{../assets/preambles/GeneralPreamble.tex}
|
||||
|
||||
|
||||
|
||||
|
||||
%----------------------------------------------------------------------------------------
|
||||
% TITLE PAGE
|
||||
%----------------------------------------------------------------------------------------
|
||||
|
||||
\title[Clinical Trials]{The Effects of Market Conditions on Recruitment and Completion of Clinical Trials}
|
||||
|
||||
\author{Will King} % Your name
|
||||
\institute[WSU] % Your institution as it will appear on the bottom of every slide, may be shorthand to save space
|
||||
{
|
||||
Washington State University \\ % Your institution for the title page
|
||||
\medskip
|
||||
\textit{william.f.king@wsu.edu} % Your email address
|
||||
}
|
||||
\date{\today} % Date, can be changed to a custom date
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
\begin{document}
|
||||
\begin{frame}
|
||||
\titlepage % Print the title page as the first slide
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
\begin{frame} %Allow frame breaks
|
||||
\frametitle{Clincial Trials} % Table of contents slide, comment this out to remove it
|
||||
% - Intro and hook (Clinical Trials are key part of pharmacological pipeline)
|
||||
Pharmaceuticals are a frequently discussed aspect of health care cost managment.
|
||||
Their development is dictated by scientific and regulatory hurdles
|
||||
including passing clinical trials
|
||||
(\cite{noauthor_fda_nodate}),
|
||||
while their market is characterized by strategic competition and ambiguous
|
||||
patent protection
|
||||
(\cite{van_der_gronde_addressing_2017}).
|
||||
|
||||
\vspace{12pt}
|
||||
|
||||
This research investigates the pathways by which market conditions
|
||||
affect clinical trial completion.
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{This research}
|
||||
\textbf{Questions:}
|
||||
\begin{enumerate}
|
||||
\item Does the existence of alternative drugs on the market make it
|
||||
harder for clinical trials to complete successfully?
|
||||
\item How much of this is occurs due to increased recruitment difficulty?
|
||||
\end{enumerate}
|
||||
|
||||
\end{frame}
|
||||
%--------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Thanks} % Table of contents slide, comment this out to remove it
|
||||
Thanks to Chris Adams and Rebecca Sachs of the Congressional Budget Office.
|
||||
\end{frame}
|
||||
%--------------------------------
|
||||
\begin{frame}[allowframebreaks] %Allow frame breaks
|
||||
\frametitle{Overview} % Table of contents slide, comment this out to remove it
|
||||
\tableofcontents
|
||||
% - Intro and hook
|
||||
% - Literature review
|
||||
% - Causal Identification
|
||||
% - Data
|
||||
% - Econometric model
|
||||
% - Results
|
||||
% - Improvements
|
||||
\end{frame}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Lit Review %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Lit Review}
|
||||
% First slide:
|
||||
%-------------------------------------------------------------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Literature Highlights}
|
||||
\begin{itemize}
|
||||
\item \cite{van_der_gronde_addressing_2017}:
|
||||
High level synthesis of overall discussion regarding drug costs.
|
||||
Both academic and non-academic sources.
|
||||
\item \cite{hwang_failure_2016}:
|
||||
Answered the question "Why do late-stage (phase III) trials fail?"
|
||||
Found that efficacy, safety, and competition reasons accounted for
|
||||
57\%, 17\%, and 22\% respectively.
|
||||
\item \cite{abrantes-metz_pharmaceutical_2004}:
|
||||
Described how drugs progress through the 3 phases of clinical trials
|
||||
and correllations between various trial characteristics and the
|
||||
clinical trial failures.
|
||||
\item \cite{khmelnitskaya_competition_2021}:
|
||||
Modeled clinical trial lifecycle of drugs, found method to separate
|
||||
scientific from competitive reasons for failure to progress to the
|
||||
next phase.
|
||||
% \item \cite{}:
|
||||
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{This research, in context}
|
||||
|
||||
In contrast to previous work looking at multiple phases of trials,
|
||||
I seek to figure out what causes individual trials to fail.
|
||||
|
||||
\vspace{12pt}
|
||||
|
||||
Instead of focusing on the drug development pipeline, I attempt to
|
||||
investigate the population of drug-based, phase III trials.
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame} %Allow frame breaks
|
||||
\frametitle{Why this approach?} % Table of contents slide, comment this out to remove it
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.8\textheight]{../assets/img/methodology_trial.png}
|
||||
\label{FIG:xkcd2726}
|
||||
\caption{``If you think THAT'S unethical, you should see the stuff we approved via our Placebo IRB.''
|
||||
- \url{https://xkcd.com/2726}
|
||||
}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Causal Identification / DGP%%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Causal Model}
|
||||
% Data Generating process
|
||||
% - Agents and their decisions
|
||||
% - Factors that influence each decision
|
||||
% -
|
||||
% -
|
||||
%-------------------------------------------------------------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Data Generating Process}
|
||||
% study sponsors
|
||||
Study Sponsors Decide to start a Phase 3 trial and whether to terminate it.
|
||||
\\
|
||||
They ask themselves:
|
||||
\begin{itemize}
|
||||
\item Do safety incidents require terminating a trial?
|
||||
\item Do efficacy results indicate the trial is worth continuing?
|
||||
\item Is recruiting sufficient to achieve our results and contain costs?
|
||||
\item Do expectations about future returns justify our expenditures?
|
||||
\end{itemize}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Data Generating Process}
|
||||
% participants
|
||||
Participants decide to enroll (and disenroll) themselves in a trial based
|
||||
\begin{itemize}
|
||||
\item Disease severity
|
||||
\item Relative safety/efficacy compared to other treatments
|
||||
\end{itemize}
|
||||
|
||||
Study sponsors plan their enrollment considering
|
||||
\begin{itemize}
|
||||
\item Total population affected
|
||||
\item Likely participant response rates
|
||||
\end{itemize}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Data Generating Process}
|
||||
% Trial Snapshots and dependencies.
|
||||
During a trial, the study sponsor reports snapshots of their trial.
|
||||
This includes updates to:
|
||||
|
||||
\begin{itemize}
|
||||
\item enrollment (actual or anticipated)
|
||||
\item current recruitment status (Recruiting, Active not recruiting, etc)
|
||||
\item study sponsor
|
||||
\item planned completion dates
|
||||
\item elapsed duration
|
||||
\end{itemize}
|
||||
|
||||
Note that final enrollment and the final status (Completed or Terminated)
|
||||
of the trial are jointly determined.
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Causal Diagram: Key Pathways}
|
||||
% Estimating Direct vs Total Effects
|
||||
\begin{figure}
|
||||
\resizebox{!}{0.5\textheight}{
|
||||
\tikzfig{../assets/tikzit/CausalGraph}
|
||||
}
|
||||
\label{FIG:CausalDiagram}
|
||||
\caption{Causal Diagram highlighting direct and total pathways}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Causal Diagram: Backdoor Crieterion}
|
||||
\small
|
||||
\begin{block}{$d$-separation}
|
||||
A set $S$ of nodes blocks a path $p$ if either
|
||||
\begin{enumerate}
|
||||
\item $p$ contains at least one arrow-emitting node in $S$
|
||||
\item $p$ contains at least one collision node $c$ that is outside $S$
|
||||
and has no descendants in $S$.
|
||||
\end{enumerate}
|
||||
If $S$ blocks all paths from X to Y, then it is said to ``$d$-separate''
|
||||
$X$ and $Y$, and then $X \perp Y | S$.
|
||||
\end{block}
|
||||
\begin{block}{Back-Door Criterion}
|
||||
A set $S$ of covariates is admisible as controls on the
|
||||
causal relationship $X \rightarrow Y$ if:
|
||||
\begin{enumerate}
|
||||
\item No element of $S$ is a decendant of $X$
|
||||
\item The elements of $S$ d-separate all paths from $X$ to $Y$ that include
|
||||
parents of $X$.
|
||||
\end{enumerate}
|
||||
\end{block}
|
||||
\cite{pearl_causality_2000}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Causal Diagram}
|
||||
Key takeaways
|
||||
\begin{itemize}
|
||||
\item Measuring enrollment prior to trial completion is necessary for causal identification.
|
||||
\item The backdoor criterion gives us the following adjustment sets:
|
||||
\begin{itemize}
|
||||
\item Total Effect for Market on Termination; Population, Condition, Phase III
|
||||
\item Direct Effects for Enrollment, Market on Termination; Population, Condition Phase III,
|
||||
Elapsed Duration, Planned Enrollment
|
||||
\end{itemize}
|
||||
\item Enrollment requires imputation
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Data %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Data}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%----------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Sources
|
||||
\subsection{Sources}
|
||||
%----------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame} %Allow frame breaks
|
||||
\frametitle{Data Sources}
|
||||
\begin{itemize}
|
||||
\item ClinicalTrials.gov - AACT \& custom scripts
|
||||
\begin{itemize}
|
||||
\item Select trials of interest
|
||||
\item Trial details:
|
||||
\begin{itemize}
|
||||
\item conditions
|
||||
\item final status
|
||||
\item drugs/interventions
|
||||
\end{itemize}
|
||||
\item Trial snapshots:
|
||||
\begin{itemize}
|
||||
\item enrollment (anticipated, planned, or actual)
|
||||
\item elapsed duration
|
||||
\item current status
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\item Medical Subject Headings (MeSH) Thesaurus
|
||||
\begin{itemize}
|
||||
\item A standardized nomenclature used to classify interventions
|
||||
and conditions in the clinical trials database.
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame} %Allow frame breaks
|
||||
\frametitle{Data Sources}
|
||||
\begin{itemize}
|
||||
\item NSDE Files (New drug code Structured product labels Data Element)
|
||||
\begin{itemize}
|
||||
\item Contains information about when a given drug was on the market.
|
||||
\end{itemize}
|
||||
\item RxNorm
|
||||
\begin{itemize}
|
||||
\item Links pharmaceuticals between MeSH standardized terms and
|
||||
NSDE files.
|
||||
\end{itemize}
|
||||
\item Global Disease Burden Survey (2019)
|
||||
\begin{itemize}
|
||||
\item Estimates of DALYs for categories of disease
|
||||
\item Links of Categories to ICD-10 Codes
|
||||
\end{itemize}
|
||||
\item ICD-10 (2019)
|
||||
\begin{itemize}
|
||||
\item WHO version
|
||||
\item CMS version (Clinical Managment)
|
||||
\item Used to group disease conditions in hierarchal model
|
||||
\end{itemize}
|
||||
\item Unified Medical Language System Thesaurus
|
||||
\begin{itemize}
|
||||
\item Used to link MeSH standardized terms and ICD-10 conditions
|
||||
\item Manual matching process
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Integration
|
||||
\subsection{Integration}
|
||||
%----------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Data Summaries}
|
||||
%put summaries now
|
||||
\begin{itemize}
|
||||
\item Number of Phase III, FDA monitored Drug Trials: 1,981
|
||||
\item Number of Trials matched to ICD-10: 186
|
||||
\item Number of Trials matched to ICD-10 with population measures: 67
|
||||
(51 completed, 16 terminated)
|
||||
\item Number of Snapshots: 616
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Data used}
|
||||
The following data points were used.
|
||||
\begin{itemize}
|
||||
\item elapsed duration
|
||||
\item asinh(number of brands)
|
||||
\item asinh(high sdi DALY estimate)
|
||||
\item asinh(high-medium sdi DALY estimate)
|
||||
\item asinh(medium sdi DALY estimate)
|
||||
\item asinh(low-medium sdi DALY estimate)
|
||||
\item asinh(low sdi DALY estimate)
|
||||
\end{itemize}
|
||||
The asinh operator was used because it parallells $\text{ln}(x)$ for
|
||||
large values of $x$ but also handles $\text{asinh}(0)=0$.
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Summaries: Trial Durations}
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_durations_hist.png}
|
||||
\label{FIG:durations}
|
||||
\caption{Trial Durations (days)}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Summaries: snapshots}
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_snapshots_hist.png}
|
||||
\label{FIG:snapshots}
|
||||
\caption{Number of Snapshots per matched trial}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Summaries: snapshots}
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.8\textheight]{../assets/img/2023-04-12_status_duration_snapshots_points.png}
|
||||
\label{FIG:snapshot_duration_scatter}
|
||||
\caption{Scatterplot of snapshot count and durations}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Econometric Model %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Econometric model}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Econometric Model}
|
||||
Estimating the total effect of brands on market
|
||||
\begin{align}
|
||||
y_n &\sim \text{Bernoulli}(p_n) \\
|
||||
p_n &= \text{logisticfn}(x_n * \beta(d_n)) \\
|
||||
\beta_k(d) &\sim \text{Normal}(\mu_k, \sigma_k) \\
|
||||
\mu_k &\sim \text{Normal}(0,1) \\
|
||||
\sigma_k &\sim \text{Gamma}(2,1)
|
||||
\end{align}
|
||||
$k$ indexes parameters and $d_n$ represets the ICD-10 group the trial corresponds to.
|
||||
\end{frame}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Results %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Results}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Results}
|
||||
Because bayesian estimation is typically done numerically, we will first
|
||||
validate convergence.
|
||||
|
||||
Then we will take a look at preliminary results.
|
||||
|
||||
Sampling details
|
||||
\begin{itemize}
|
||||
\item 6 chains
|
||||
\item 2,500 warmup, 2,500 sampling runs
|
||||
\item seed = 11021585
|
||||
\end{itemize}
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Convergence Tests
|
||||
\subsection{Convergence}
|
||||
%----------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Warnings}
|
||||
|
||||
\begin{itemize}
|
||||
\item There were no diverging transitions.
|
||||
\item There were 15,000 transitions that exceeded max treedepth.
|
||||
Sampling efficiency is poor.
|
||||
\item All chains had low Bayesian Fraction of Missing Information.
|
||||
Some areas of the distribution were poorly explored.
|
||||
\item R-hat = $1.23$, ideal is around 1, chains did not mix well.
|
||||
\item Bulk and Tail Effective Sample sizes were low,
|
||||
suggesting mean and variance/quantile estimates will be unreliable.
|
||||
\end{itemize}
|
||||
\cite{mc-stan}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Convergence: Mu}
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.9\textheight]{../assets/img/2023-04-11_mu_points.png}
|
||||
\label{FIG:caption}
|
||||
\caption{Hyperparameter Points Plots: Mu}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Convergence: Sigma}
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_points.png}
|
||||
\label{FIG:caption}
|
||||
\caption{Hyperparameter Points Plots: Sigma}
|
||||
\end{figure}
|
||||
\end{frame}
|
||||
%----------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Preliminary Results
|
||||
\subsection{Preliminary Results}
|
||||
%----------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Preliminary Results: Mu}
|
||||
|
||||
\begin{columns}
|
||||
\begin{column}{0.3\textwidth}
|
||||
\begin{enumerate}
|
||||
\item elapsed duration
|
||||
\item asinh(n\_brands)
|
||||
\item asinh(high sdi)
|
||||
\item asinh(high-medium sdi)
|
||||
\item asinh(medium sdi)
|
||||
\item asinh(low-medium sdi)
|
||||
\item asinh(low sdi)
|
||||
\end{enumerate}
|
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\end{column}
|
||||
\begin{column}{0.7\textwidth}
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_mu_dist.png}
|
||||
\label{FIG:caption}
|
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\caption{Hyperparameter Distribution: Mu}
|
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\end{figure}
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\end{column}
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\end{columns}
|
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\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Preliminary Results: Sigma}
|
||||
|
||||
\begin{figure}
|
||||
\includegraphics[height=0.8\textheight]{../assets/img/2023-04-11_sigma_dist.png}
|
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\label{FIG:caption}
|
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\caption{Hyperparameter Distribution: Sigma}
|
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\end{figure}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Interpretation}
|
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All of the following interpretations are done in the context of insufficient data
|
||||
|
||||
\begin{enumerate}
|
||||
\item Elapsed Duration (Mu[1]): Trending Negative, reduced probability of termination.
|
||||
\item Number of Brands(Mu[2]): Trending Positive, increased probability of termination.
|
||||
\item Population Measures (Mu[3]-Mu[7])
|
||||
\begin{enumerate}
|
||||
\item What is most surprising is that these are both positive and negative.
|
||||
Probably need more data.
|
||||
\end{enumerate}
|
||||
\item It is surprising to see the wide distribution in sigma values.
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%%%%%%%%%%%%%%%%%%%% Improvements %%%%%%%%%%%%%%%%%%%%%%%%
|
||||
\section{Improvements}
|
||||
%-------------------------------------------------------------------------------------
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Proposed improvements}
|
||||
\begin{enumerate}
|
||||
\item Match more trials to ICD-10 codes
|
||||
\item Improve Measures of Market Conditions
|
||||
\item Adjust Covariance Structure
|
||||
\item Find Reasonable Priors
|
||||
\item Remove disease categories that don't exist in the data from the priors
|
||||
\item Imputing Enrollment
|
||||
\item Improve Population Estimates
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}
|
||||
\frametitle{Questions?}
|
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\center{\huge{Questions?}}
|
||||
|
||||
\end{frame}
|
||||
%-------------------------------
|
||||
\begin{frame}[allowframebreaks]
|
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\frametitle{Bibliography}
|
||||
\printbibliography
|
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\end{frame}
|
||||
%-------------------------------
|
||||
\end{document}
|
||||
%=========================================
|
||||
%\begin{frame}
|
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% \frametitle{MarginalRevenue}
|
||||
% \begin{figure}
|
||||
% \tikzfig{../Assets/owned/ch8_MarginalRevenue}
|
||||
% \includegraphics[height=\textheight]{../Assets/copyrighted/KrugmanObsterfeldMeliz_fig8-7.jpg}
|
||||
% \label{FIG:costs}
|
||||
% \caption{Average Cost Curve as firms enter.}
|
||||
% \end{figure}
|
||||
%\end{frame}
|
||||
%-------------------------------
|
||||
%\begin{frame}
|
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% \frametitle{Columns}
|
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% \begin{columns}
|
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% \begin{column}{0.5\textwidth}
|
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% \end{column}
|
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% \begin{column}{0.5\textwidth}
|
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% \begin{figure}
|
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% \tikzfig{../Assets/owned/ch7_EstablishedAdvantageExample2}
|
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% \label{FIG:costs}
|
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% \caption{Setting the Stage}
|
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% \end{figure}
|
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% \end{column}
|
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% \end{columns}
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%\end{frame}
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% %---------------------------------------------------------------
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